6.4 Converting Mass and Particles
Notes
To go between grams and particles, go through moles: grams to moles to particles.
- $\displaystyle \text{grams} \times \frac{1 \text{ mol}}{\text{molar mass}} \times \frac{6.02 \times 10^{23}}{1 \text{ mol}} = \text{particles}$.
- To count atoms inside molecules, multiply by the number of atoms per molecule. One $\text{H}_2\text{O}$ molecule has 3 atoms.
- Example: 9.01 g $\text{H}_2\text{O}$ $= 0.500$ mol $= 3.01 \times 10^{23}$ molecules, which contain $3 \times 3.01 \times 10^{23} = 9.03 \times 10^{23}$ atoms.
Practice
How many atoms are in 1.00 g of gold? (Au = 196.97)
$\displaystyle \frac{1.00}{196.97} = 5.08 \times 10^{-3}$ mol, and $5.08 \times 10^{-3} \times 6.02 \times 10^{23} = 3.06 \times 10^{21}$ atoms.
What is the mass of $1.20 \times 10^{24}$ atoms of iron? (Fe = 55.85)
$\displaystyle \frac{1.20 \times 10^{24}}{6.02 \times 10^{23}} = 1.99$ mol, and $1.99 \times 55.85 = 111$ g.
How many hydrogen atoms are in 0.500 mol of $\text{CH}_4$?
Molecules $= 0.500 \times 6.02 \times 10^{23} = 3.01 \times 10^{23}$. Each has 4 H atoms: $4 \times 3.01 \times 10^{23} = 1.20 \times 10^{24}$.
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